# A tree increases annually by 1/8 of its height. By how much will it increase after 2½ years. If its length today is 8 m.? - Mathematics and Statistics

Sum

A tree increases annually by 1/8 of its height. By how much will it increase after 2½ years. If its length today is 8 m.?

#### Solution

The height of the tree today is 8 m.

The height of the tree increases by (1/8)^"th" of its height every year.

At the end of the 1st year, the height of the tree will be

= 8 + 1/8 xx 8

= 9 m

And, at the end of the 2nd year, the height of the tree will be

= 9 + 1/8 xx 9 = 9(1 + 1/8)

= 9 xx 9/8 = 81/8

After six more months, the height of the tree will be = 81/8 + 1/16(81/8)

= 81/8(1 + 1/16)

= 81/8 xx 17/16

= 10.75 m

∴ Increase in the height of the tree after 2^(1/2) years = 10.75 – 8 = 2.75 m.

Concept: Depreciation
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#### APPEARS IN

Balbharati Mathematics and Statistics 2 (Commerce) 11th Standard HSC Maharashtra State Board
Chapter 9 Commercial Mathematics
Miscellaneous Exercise 9 | Q 10 | Page 144